9,219 reputation
51108
bio website linkedin.com/in/nikov
location Redmond, WA
age 35
visits member for 2 years, 8 months
seen 29 mins ago

Having more than 12 years of experience in software development and testing, I currently work as SDE 2 at Microsoft on the ".NET Compiler Platform" project (a.k.a. "Roslyn") — the next generation of managed C# and VB.NET compilers, programming language tools and IDE. Among other things, my job involves participation in design of type systems and new language features, checking them for soundness and their actual implementation and testing.

I am also a member of TC49-TG2 (Ecma standardization committee for C#), currently working on the next version of the international standard Ecma-334.

Although I am not a professional mathematician, I hold a degree in theoretical physics, and I am very passionate about mathematics, especially about evaluation of integrals, sums and products in a closed form, foundations of mathematics, order theory, type theory, computability theory, graph theory and combinatorics.

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Feel free to contact me at <ɯoɔ·ןᴉɐɯᵷ(ʇɐ)ʌoʞᴉuʇǝɥsǝɹ·ʌ>


23m
accepted Prove ${\large\int}_0^\infty\left({_2F_1}\left(\frac16,\frac12;\frac13;-x\right)\right)^{12}dx\stackrel{\color{#808080}?}=\frac{80663}{153090}$
54m
revised Prove ${\large\int}_0^\infty\left({_2F_1}\left(\frac16,\frac12;\frac13;-x\right)\right)^{12}dx\stackrel{\color{#808080}?}=\frac{80663}{153090}$
added 683 characters in body
16h
comment Prove ${\large\int}_0^\infty\left({_2F_1}\left(\frac16,\frac12;\frac13;-x\right)\right)^{12}dx\stackrel{\color{#808080}?}=\frac{80663}{153090}$
I suspect that the integrand might be an elementary function. It seems to have algebraic values at algebraic points.
17h
asked Prove ${\large\int}_0^\infty\left({_2F_1}\left(\frac16,\frac12;\frac13;-x\right)\right)^{12}dx\stackrel{\color{#808080}?}=\frac{80663}{153090}$
23h
accepted Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$
1d
awarded  Nice Question
1d
reviewed Approve suggested edit on Solve for $x$, $\tan x +\sec x = 2\cos x$ ; $−∞ < x < ∞$
1d
comment Convergence of ${\large\int}_{-\infty}^\infty J_0(x)\,J_0(x+a)\,dx$
Unfortunately, I cannot reliably verify this conjecture because of very slow convergence of numerical integration (and significant error in the result). How did you come up with it?
1d
asked Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$
1d
comment Integral ${\large\int}_0^\infty\frac{\ln x}{1+x}\sqrt{\frac{x+\sqrt{1+x^2}}{1+x^2}}\ dx$
@Lucian I simplified the result to 3 lines with only 1 PolyLog term, but it still looks bad...
Jul
22
asked Convergence of ${\large\int}_{-\infty}^\infty J_0(x)\,J_0(x+a)\,dx$
Jul
22
comment Packing an infinite sequence of disks
@achillehui Great answer, thanks!
Jul
21
comment Derivative of a generalized hypergeometric function
Search for a closed form for the numeric value of $f'(0)$ suggests $\displaystyle\frac{\text{Ci}(2\pi)-\ln(2\pi)-\gamma}{\pi^2}$ (agrees to at least 1000 decimal digits).
Jul
21
awarded  Nice Question
Jul
15
revised Packing an infinite sequence of disks
added 89 characters in body
Jul
13
asked Packing an infinite sequence of disks
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
29
awarded  Favorite Question
Jun
28
awarded  Necromancer